Finite Group Databasebeta

← #14283004

Subgroups — #14283004

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5627C211yesmaximal, characteristic
2D3×#3963C211yesmaximal, characteristic, complemented
3#11748505C211yesmaximal, characteristic, complemented
4#11746359C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10602501—31nomaximal, Hall
9C2×C5×#239C411yescharacteristic, complemented
10C22×C4×C5×D3C2211yescharacteristic
11C22×D3×Dic5—21no—
12C3×C5×C22⋊Q8C2211yescharacteristic
13C5×#946C411yescharacteristic, complemented
14C5×#930C2211yescharacteristic
15C5×#895C411yescharacteristic, complemented
16C5×#894—21no—
17C5×#893—21no—
18C5×#892C411yescharacteristic, complemented
19C5×#882—21no—
20C5×#67⋊C4—21no—
21C2×#6650—21no—
22#91115C2211yescharacteristic
23#91114C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90994—21no—
27(C2×D3)⋊#168—21no—
28#68334—51nomaximal, Hall
29C5×#525—31no—
30C2×#3963—31no—
31#65496—31no—
32#64758—31no—
33#64758D311yescharacteristic, complemented
34#64757—31no—
35#64757—31no—
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C22×C5×Dic3D411yescharacteristic
42C5×#239—42no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12C2×C411yescharacteristic, complemented
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3—42no—
48C2×C4×C5×D3C2×C411yescharacteristic
49C2×C4×C5×D3C2×C411yescharacteristic
50C2×C4×C5×D3D411yescharacteristic
51C2×C4×C5×D3D411yescharacteristic
52C22×C3×Dic5—21no—
53C2×D3×Dic5—24no—
54C2×D3×Dic5—42no—
55C2×D3×Dic5—42no—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
58C3×C5×C22⋊C4—21no—
59C2×C3⋊#168—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×C4⋊Dic3C2×C411yescharacteristic, complemented
65C5×Dic3⋊C4—21no—
66C4×C5×Dic3—21no—
67C2×C3×#168—21no—
68#6650—42no—
69#5627D511yescharacteristic
70#4726—51no—
71D3×#95—51no—
72C3×#328—51no—
73#4538—51no—
74#4470—51no—
75#4451—51no—
76C2×C5×#41—31no—
77C23×C4×C5—31no—
78C23×Dic5—61no—
79C5×#123—61no—
80C5×C22⋊Q8—31no—
81C5×C22⋊Q8C2×D311yescharacteristic
82C5×#121—31no—
83C5×#121—31no—
84C5×#120—61no—
85C4×C5×D4—61no—
86C4×C5×D4—61no—
87C5×#117—31no—
88C2×#681—61no—
89#3963—31no—
90#3963—61no—
91#3963C2×D311yescharacteristic
92C22⋊#168—31no—
93C22⋊#168—61no—
94C22⋊#168C2×D311yescharacteristic
95#1504—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—22no—
100C22×C5×D3—22no—
101C22×C5×D3—21no—
102C22×C5×D3C22⋊C411yescharacteristic
103C22×C5×D3C22⋊C411yescharacteristic
104C3×C5×Q8—41no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C5×#67—41no—
114C5×#67—41no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C5×D12—41no—
120C5×D12—42no—
121C5×D12—42no—
122C4×C5×D3—22no—
123C4×C5×D3—22no—
124C4×C5×D3—41no—
125C4×C5×D3—41no—
126C4×C5×D3—42no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130D3×Dic5—48no—
131C3⋊#168—41no—
132C3×#168—41no—
133C2×#239Dic511yescharacteristic, complemented
134C22×C4×D3—101no—
135C22×C4×D3C2×D511yescharacteristic
136C3×C22⋊Q8C2×D511yescharacteristic
137#946Dic511yescharacteristic, complemented
138#930C2×D511yescharacteristic
139C2×ΓL(1,𝔽25)—101no—
140#895Dic511yescharacteristic, complemented
141#894—21no—
142#893—21no—
143#892Dic511yescharacteristic, complemented
144#882—21no—
145#67⋊C4—21no—
146C3×C22⋊C8—51no—
147C3×#95—51no—
148C3⋊#95—51no—
149C3⋊#95—101no—
150#830—51no—
151(C2×D3)⋊C8—101no—
152C24×C5—31no—
153C5×#41—122no—
154C2×C5×Q8C4×D311yescharacteristic, complemented
155C2×C5×D4—31no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C2×C5×D4—61no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—61no—
165C22×C4×C5—122no—
166C22×C4×C5C22×D311yescharacteristic
167C22×Dic5—21no—
168C22×Dic5—64no—
169C22×Dic5—61no—
170C22×Dic5—122no—
171C22×Dic5—122no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—31no—
174C5×C4⋊C4—61no—
175C5×C4⋊C4C4×D311yescharacteristic, complemented
176C5×C22⋊C4—21no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181C42×C5—61no—
182#681—122no—
183C2×#168—21no—
184C2×#168—61no—
185#525—31no—
186#407—151no—
187C2×#95—151no—
188#328—51no—
189#328—151no—
190#327—151no—
191#327—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
196C22×C3×C5#13711yescharacteristic
197C2×C5×D3—24no—
198C2×C5×D3—24no—
199C2×C5×D3—21no—
200C2×C5×D3—21no—
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3—41no—
204C2×C5×D3—41no—
205C2×C5×D3—41no—
206C2×C5×D3#9912yes—
207C2×C5×D3#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—41no—
212Dic15—42no—
213C3×Dic5—42no—
214C5×Dic3—21no—
215C5×Dic3—21no—
216C5×Dic3—41no—
217C23×D3C22⋊D511yescharacteristic
218C2×C3×Q8C2×Dic511yescharacteristic, complemented
219C22×C3×C4—101no—
220C22×C3×C4C22×D511yescharacteristic
221C2×#67—21no—
222C22×Dic3—101no—
223C22×Dic3C22⋊D511yescharacteristic
224#239—42no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12C2×Dic511yescharacteristic, complemented
228C2×C4×D3—21no—
229C2×C4×D3—42no—
230C2×C4×D3—104no—
231C2×C4×D3—202no—
232C2×C4×D3—202no—
233C2×C4×D3C2×Dic511yescharacteristic
234C2×C4×D3C2×Dic511yescharacteristic
235C2×C4×D3C22⋊D511yescharacteristic
236C2×C4×D3C22⋊D511yescharacteristic
237C2×C3×C8—101no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4C2×Dic511yescharacteristic, complemented
240C3×C22⋊C4—21no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—21no—
245C4⋊Dic3C2×Dic511yescharacteristic, complemented
246Dic3⋊C4—21no—
247C4×Dic3—21no—
248C2×C3⋊C8—101no—
249ΓL(1,𝔽25)—202no—
250C23×C5—31no—
251C23×C5—31no—
252C23×C5—62no—
253C23×C5—62no—
254C23×C5—61no—
255C23×C5—61no—
256C23×C5—61no—
257C23×C5D3×D411yescharacteristic
258C5×Q8—41no—
259C5×D4—121no—
260C5×D4—122no—
261C5×D4—122no—
262C5×D4—121no—
263C5×D4—121no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—31no—
267C2×C4×C5—31no—
268C2×C4×C5—41no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5—61no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5—122no—
275C2×C4×C5—121no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×Dic5—22no—
279C2×Dic5—41no—
280C2×Dic5—41no—
281C2×Dic5—62no—
282C2×Dic5—128no—
283C2×Dic5—121no—
284C2×Dic5—121no—
285#168—41no—
286#168—121no—
287C2×#41—31no—
288C23×C4—31no—
289C23×C4—301no—
290C2×M16—301no—
291#123—61no—
292C22⋊Q8—31no—
293C22⋊Q8D3×D511yescharacteristic
294#121—31no—
295#121—31no—
296#120—61no—
297C4×D4—61no—
298C4×D4—61no—
299#117—31no—
300C22⋊C8—51no—
301C22⋊C8—151no—
302C22⋊C8—301no—
303#95—51no—
304#95—151no—
305#95—301no—
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×#9911yescharacteristic
309C2×C3×C5#41711yescharacteristic
310C2×C3×C5C2×#10411yescharacteristic
311C5×D3—22no—
312C5×D3—22no—
313C5×D3—81no—
314C23×C3C2×C22⋊D511yescharacteristic
315C22×D3—21no—
316C22×D3—21no—
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—21no—
320C22×D3C22⋊Dic511yescharacteristic
321C22×D3C22⋊Dic511yescharacteristic
322C3×Q8—41no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—102no—
327C2×C3×C4—201no—
328C2×C3×C4—201no—
329C2×C3×C4C22×Dic511yescharacteristic
330C2×C3×C4C2×C22⋊D511yescharacteristic
331#67—41no—
332#67—41no—
333C2×Dic3—21no—
334C2×Dic3—41no—
335C2×Dic3—102no—
336C2×Dic3—201no—
337C2×Dic3—201no—
338C2×Dic3C22⋊Dic511yescharacteristic
339C2×Dic3C22⋊Dic511yescharacteristic
340D12—41no—
341D12—42no—
342D12—42no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—41no—
346C4×D3—41no—
347C4×D3—42no—
348C4×D3—208no—
349C3×C8—201no—
350C3⋊C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—32no—
354C22×C5—32no—
355C22×C5—64no—
356C22×C5—64no—
357C22×C5—61no—
358C22×C5—61no—
359C22×C5—61no—
360C22×C5—61no—
361C22×C5—121no—
362C22×C5—121no—
363C22×C5—121no—
364C22×C5D3×C22⋊C411yescharacteristic
365C22×C5#91411yescharacteristic
366C22×C5#91811yescharacteristic
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—41no—
370C4×C5—41no—
371C4×C5—61no—
372C4×C5—61no—
373C4×C5—121no—
374Dic5—42no—
375Dic5—122no—
376C24—31no—
377#41—122no—
378C2×Q8D3×Dic511yescharacteristic, complemented
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4—61no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—61no—
389C22×C4—101no—
390C22×C4—122no—
391C22×C4—304no—
392C22×C4—301no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—602no—
397C2×C8—101no—
398C2×C8—301no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—61no—
402C4⋊C4D3×Dic511yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C42—61no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3#409511yescharacteristic
413C22×C3#409711yescharacteristic
414C22×C3C2×C22⋊Dic511yescharacteristic
415C2×D3—24no—
416C2×D3—24no—
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—21no—
420C2×D3—21no—
421C2×D3—41no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3#396612yes—
425C2×D3#396912yes—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—202no—
431Dic3—21no—
432Dic3—21no—
433Dic3—41no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—62no—
438C2×C5—62no—
439C2×C5—241no—
440C2×C5D3×#9911yescharacteristic
441C2×C5#480311yescharacteristic
442C2×C5D3×#10411yescharacteristic
443C23—31no—
444C23—31no—
445C23—62no—
446C23—62no—
447C23—61no—
448C23—61no—
449C23—61no—
450C23D3×C22⋊D511yescharacteristic
451Q8—41no—
452D4—121no—
453D4—122no—
454D4—122no—
455D4—121no—
456D4—121no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—41no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—61no—
465C2×C4—102no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—122no—
469C2×C4—121no—
470C2×C4—201no—
471C2×C4—201no—
472C2×C4—302no—
473C2×C4—608no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4C2×D3×Dic511yescharacteristic
477C2×C4D3×C22⋊D511yescharacteristic
478C8—201no—
479C8—601no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3C2×#396611yescharacteristic
483C2×C3#6552111yescharacteristic
484C2×C3C2×#396911yescharacteristic
485D3—22no—
486D3—22no—
487D3—81no—
488C5#6833411yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—32no—
492C22—32no—
493C22—64no—
494C22—64no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22#9150411yescharacteristic
503C22#9151011yescharacteristic
504C22D3×C22⋊Dic511yescharacteristic
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—61no—
510C4—61no—
511C4—121no—
512C4—202no—
513C4—602no—
514C3#1060250111yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—62no—
518C2—62no—
519C2—241no—
520C2D3×#396611yescharacteristic
521C2#1174920111yescharacteristic
522C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5627C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D3×#3963C2semidirect
3. #11748505C2semidirect
4. #11746359C2semidirect
5. C3×#64758C2semidirect
6. #11745957C2semidirect
7. #11745956C2semidirect
9. C2×C5×#239C4semidirect
13. C5×#946C4semidirect
15. C5×#895C4semidirect
18. C5×#892C4semidirect
33. #64758D3semidirect
37. C2×C3×C5×Q8C2×C4semidirect
45. C2×C5×D12C2×C4semidirect
57. C3×C5×C4⋊C4C2×C4semidirect
64. C5×C4⋊Dic3C2×C4semidirect
133. C2×#239Dic5semidirect
137. #946Dic5semidirect
140. #895Dic5semidirect
143. #892Dic5semidirect
154. C2×C5×Q8C4×D3semidirect
175. C5×C4⋊C4C4×D3semidirect
218. C2×C3×Q8C2×Dic5semidirect
227. C2×D12C2×Dic5semidirect
239. C3×C4⋊C4C2×Dic5semidirect
245. C4⋊Dic3C2×Dic5semidirect
378. C2×Q8D3×Dic5semidirect
402. C4⋊C4D3×Dic5semidirect
409. C3×C5#1504semidirect
488. C5#68334semidirect
514. C3#10602501semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#56272
D3×#39632
#117485052
#117463592
C3×#647582
#117459572
#117459562
#106025013
#683345